Chapter 3.3, Problem 40PPS

To determine

To estimate the slope of the given object in figure using a ruler.

Answer to Problem 40PPS

  $-\frac{1}{2}$

Explanation of Solution

Given:

The figures:

  

Concept Used:

Equation of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given by $y-y_1=m\left(x-x_1\right)$ , where $\text{slope, }m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

The slope of any line is given by rise over run. That is, the ratio of the number of units it rise or fall over the number of units it move forward or backward from a fixed point.

In the given figure we can see that from the left corner the object move down and then move forward to reach to right corner of the object.

Also observe that the distance move down is approximately half of the distance moved forward.

Since it move down, so the rise would be negative. So, the slope of the object is

  $\begin{array}{c}\text{slope, }m=\frac{\text{rise}}{\text{run}}\end{array}$

      $\begin{array}{c}=\frac{-1}{2}\end{array}$

      $\begin{array}{c}=-\frac{1}{2}\end{array}$

Thus, the slope of the given object is $-\frac{1}{2}$ .